Six transmit antenna codebook design

ABSTRACT

A method of wireless data transmission includes a base station having six antennas and at least one user equipment. The base station forms at least one layer of data stream including modulated symbols, precodes the at least one layer of data stream via multiplication with consecutive first and second precoding matrices and transmit the precoded data stream to the at least one user equipment via the six antennas. The first precoding matrix W 1  is a block diagonal matrix formed by two identical 3 by Nb matrices, where Nb is the number of distinct Discrete Fourier Transform vectors. The second precoding matrix W 2  introduces a phase shift between the two 3 by Nb matrices and selects a column subset from the first precoding matrix.

CLAIM OF PRIORITY

This application claims priority under 35 U.S.C. 119(e)(1) to U.S.Provisional Application No. 61/478,599 filed Apr. 25, 2011.

TECHNICAL FIELD OF THE INVENTION

The technical field of this invention is wireless communication such aswireless telephony.

BACKGROUND OF THE INVENTION

The present embodiments relate to wireless communication systems and,more particularly, to the precoding of Physical Downlink Shared Channel(PDSCH) data and dedicated reference signals with codebook-basedfeedback for multi-input multi-output (MIMO) transmissions.

With Orthogonal Frequency Division Multiplexing (OFDM), multiple symbolsare transmitted on multiple carriers that are spaced apart to provideorthogonality. An OFDM modulator typically takes data symbols into aserial-to-parallel converter, and the output of the serial-to-parallelconverter is considered as frequency domain data symbols. The frequencydomain tones at either edge of the band may be set to zero and arecalled guard tones. These guard tones allow the OFDM signal to fit intoan appropriate spectral mask. Some of the frequency domain tones are setto values which will be known at the receiver. Among these areCell-specific Channel State Information Reference Signals (CSI-RS) andDedicated or Demodulating Reference Signals (DMRS). These referencesignals are useful for channel estimation at the receiver. In amulti-input multi-output (MIMO) communication systems with multipletransmit/receive antennas, the data transmission is performed viaprecoding. Here, precoding refers to a linear (matrix) transformation ofa L-stream data into P-stream where L denotes the number of layers (alsotermed the transmission rank) and P denotes the number of transmitantennas. With the use of dedicated (user-specific) DMRS, a transmitter(base station, also termed eNodeB can perform any precoding operationwhich is transparent to a user equipment (UE) which acts as a receiver.At the same time, it is beneficial for the base station to obtain arecommendation on the choice of precoding matrix from the userequipment. This is particularly the case for frequency-divisionduplexing (FDD) where the uplink and downlink channels occupy differentparts of the frequency bands, i.e. the uplink and downlink are notreciprocal. Hence, a codebook-based feedback from the UE to the eNodeBis preferred. To enable a codebook-based feedback, a precoding codebookneeds to be designed.

To extend cell coverage and service over a wide area, employing remoteradio heads (RRHs) is beneficial. Multiple units of RRH are distributedover a wide area and act as multiple distributed antennas for theeNodeB. For downlink transmissions, each RRH unit is associated with aunit of transmit radio device—which constitutes to at least one antennaelement along with the associated radio and analog front-end devices.Each unit of RRH is positioned relatively far from the eNodeB andtypically connected via a low-latency line such as fiber optic link.Some exemplary configurations are depicted in FIG. 1 where six RRHs areutilized. Depending on whether each RRH is equipped with a single ordual antenna elements, up to 12 antenna elements can be supported.

While the LTE cellular standardization along with its further evolutionLTE-Advanced (also known as the E-UTRA and further enhanced E-UTRA,respectively) offer a solid support of codebook-based precoding, thecurrent (Rel.10/11) specification only supports precoding for 2, 4, and8 antenna elements. From FIG. 2, it is expected that the number oftransmit antenna elements changes depending on the number of RRHs. Whilea downlink transmission with more than 8 antennas may not be necessary,six-antenna transmission is easily envisioned and justified ifreasonable flexibility is desired.

While the preceding approaches provide improvements in wirelesscommunications, the present inventors recognize that still furtherimprovements in downlink (DL) spectral efficiency are possible whenRRH-based configuration is employed. In particular, a 6-antennaprecoding codebook design is invented to improve transmissionflexibility. Accordingly, the preferred embodiments described below aredirected toward these problems as well as improving upon the prior art.While the preceding approaches provide steady improvements in wirelesscommunications, the present inventors recognize that still furtherimprovements in downlink (DL) spectral efficiency are possible.Accordingly, the preferred embodiments described below are directedtoward these problems as well as improving upon the prior art.

SUMMARY OF THE INVENTION

A method of wireless data transmission includes a base station havingsix antennas and at least one user equipment. The base station forms atleast one layer of data stream including modulated symbols, precodes theat least one layer of data stream via multiplication with consecutivefirst and second precoding matrices and transmit the precoded datastream to the at least one user equipment via the six antennas.

The first precoding matrix W₁ is a block diagonal matrix formed by twoidentical 3 by Nb matrices, where Nb is the number of distinct DiscreteFourier Transform vectors. The set of all the possible first precodingmatrices W1 are as follows:

${B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \cdots \mspace{14mu} b_{11}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\frac{2\pi \; {mn}}{12}}},{m = 0},1,{{2\mspace{14mu} n} = 0},1,\cdots,11.$X^((k)) ∈ {[b_((3k)mod 12)  b_((3k + 1)mod 12)  ⋯  b_((3k + 5)mod 12)]:  k = 0, 1, 2, 3}${W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}$

The second precoding matrix W₂ introduces a phase shift between the two3 by Nb matrices and selects a column subset from the first precodingmatrix. The set of all the possible second precoding matrices W₂ are asfollows:

${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},{Y \in {\left\{ {e_{1},e_{2},\cdots,e_{6}} \right\}.}}$

BRIEF DESCRIPTION OF THE DRAWINGS

These and other aspects of this invention are illustrated in thedrawings, in which:

FIG. 1 illustrates an exemplary prior art wireless communication systemto which this application is applicable;

FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA)Time Division Duplex (TDD) frame structure of the prior art;

FIG. 3 is a simplified block diagram describing a precoder selectionmechanism at the receiver (UE) based on the dual-stage codebook; and

FIG. 4 is a block diagram illustrating internal details of a basestation and a mobile user equipment in the network system of FIG. 1suitable for implementing this invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

FIG. 1 shows an exemplary wireless telecommunications network 100. Theillustrative telecommunications network includes base stations 101, 102and 103, though in operation, a telecommunications network necessarilyincludes many more base stations. Each of base stations 101, 102 and 103(eNB) are operable over corresponding coverage areas 104, 105 and 106.Each base station's coverage area is further divided into cells. In theillustrated network, each base station's coverage area is divided intothree cells. Handset or other user equipment (UE) 109 is shown in Cell A108. Cell A 108 is within coverage area 104 of base station 101. Basestation 101 transmits to and receives transmissions from UE 109. As UE109 moves out of Cell A 108 and into Cell B 107, UE 109 may be handedover to base station 102. Because UE 109 is synchronized with basestation 101, UE 109 can employ non-synchronized random access toinitiate handover to base station 102.

Non-synchronized UE 109 also employs non-synchronous random access torequest allocation of up-link 111 time or frequency or code resources.If UE 109 has data ready for transmission, which may be traffic data,measurements report, tracking area update, UE 109 can transmit a randomaccess signal on up-link 111. The random access signal notifies basestation 101 that UE 109 requires up-link resources to transmit the UEsdata. Base station 101 responds by transmitting to UE 109 via down-link110, a message containing the parameters of the resources allocated forUE 109 up-link transmission along with a possible timing errorcorrection. After receiving the resource allocation and a possibletiming advance message transmitted on down-link 110 by base station 101,UE 109 optionally adjusts its transmit timing and transmits the data onup-link 111 employing the allotted resources during the prescribed timeinterval.

Base station 101 configures UE 109 for periodic uplink soundingreference signal (SRS) transmission. Base station 101 estimates uplinkchannel quality information (CSI) from the SRS transmission.

FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA)time division duplex (TDD) Frame Structure. Different subframes areallocated for downlink (DL) or uplink (UL) transmissions. Table 1 showsapplicable DL/UL subframe allocations.

TABLE 1 Config- Switch-point Sub-frame number uration periodicity 0 1 23 4 5 6 7 8 9 0  5 ms D S U U U D S U U U 1  5 ms D S U U D D S U U D 2 5 ms D S U D D D S U D D 3 10 ms D S U U U D D D D D 4 10 ms D S U U DD D D D D 5 10 ms D S U D D D D D D D 6 10 ms D S U U U D S U U D

A precoding structure that fulfills properties 1 and 2 separates thelong-term and short-term components of the precoder. Long-term andshort-term refer to the need for feedback interval or time granularitywhich may be associated with frequency granularity as well. Thelong-term component does not need high frequency granularity while theshort-term component may need higher frequency granularity. A particularstructure of interest known as a dual-stage precoder is as follows:

W=ƒ(W ₁ ,W ₂)   (1)

where: W₁ is the long-term component; and W₂ is the short-termcomponent. Each component is assigned a codebook. Thus two distinctcodebooks CB₁ and CB₂ are needed. W₁ adapts to the long-term channelstatistics such as the spatial covariance matrix. W₂ adapts to theshort-term channel properties such as phase adjustment needed tocounteract short-term fading. For this structure the feedback overheadcan be potentially reduced as compared to a one-stage counterpart sinceW₁ does not need to be updated as often as W₂. An example of the matrixfunction f( . , . ) includes a product (matrix multiplication) functionf(x,y)=xy or the Kronecker product function f(x,y)=x{circle around(×)}y.

The choice of W₁ from a size-N codebook is enumerated by a precodingmatrix indicator PMI₁. The choice of W₂ from a size-M2 codebook isenumerated by a precoding matrix indicator PMI₂. Essentially, the finalprecoding matrix/vector is a function of two PMIs:

W=ƒ(PMI ₁,PMI₂)   (2)

PMI₁ is updated in a significantly less frequent rate than PMI₂. Inaddition, PMI₁ is intended for the entire system bandwidth while PMI₂can be frequency-selective. FIG. 3 illustrates this overall concept.

FIG. 3 illustrates the technique used in downlink LTE-Advanced (LTE-A).The UE selects PMI₁ and PMI₂ and hence W₁ and W₂ in a manner similar tothe LTE feedback paradigm.

The UE first selects the first precoder codebook W₁ (block 311) based onthe long-term channel properties such as spatial covariance matrix suchas in a spatial correlation domain from an input of PMI₁. This is donein a long-term basis consistent with the fact that spatial covariancematrix needs to be estimated over a long period of time and in awideband manner.

Conditioned upon W₁, the UE selects W₂ based on the short-term(instantaneous) channel. This is a two stage process. Block 312 selectsone of a set of codebooks CB₂ ⁽⁰⁾ to CB₂ ^((N−1)) based upon the PMI₁input. Block 312 selects one predecoder corresponding to the selectedcodebook CB₂ ^((PMI) ₁ ⁾ and PMI₂. This selection may be conditionedupon the selected rank indicator (RI). -Alternatively, RI can beselected jointly with W₂. Block 314 takes the selected W₁ and W₂ andforms the function f(W₁, W₂).

PMI₁ and PMI₂ are reported to the base station (eNodeB or eNB) atdifferent rates and/or different frequency resolutions.

For the rest of this application assume the following product matrixprecoder:

W=ƒ(W ₁,W₂)=W ₁W₂   (3)

Two alternatives for the block diagonal designs for W₁ are given asfollows. The first alternative uses a non-overlapping adjacent beamdesign W₁. Note that C₁ is used instead of CB₁ to represent the codebookfor W₁. W₁ is a block diagonal matrix of X where X is a 3 by Nb matrixand Nb denotes the number of adjacent 3Tx Discrete Fourier Transform(DFT) beams contained in X. This design is able to synthesize N 3Tx DFTbeams within each polarization group. For a given N, the spatialoversampling factor is essentially N/3. The overall 3Tx DFT beamcollections are captured in the 3 by N matrix B. Using co-phasing in W₂described below, the composite precoder W can synthesize up to N 6Tx DFTbeams. In that case, N=12 or 24 is a good candidate. The set of W₁matrices represents (N/Nb) level partitioning (hence non-overlapping) ofthe N 3Tx beam angles (in X each polarization group). This designresults in a codebook size of (N/Nb) for W₁.

$\begin{matrix}{{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \cdots \mspace{14mu} b_{N - 1}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\frac{2\pi \; {mn}}{N}}},{m = 0},1,{{2\mspace{14mu} n} = 0},1,\cdots,{N - 1}}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({N_{b}k})}{mod}\; N}\mspace{14mu} b_{{({{N_{b}k} + 1})}{mod}\; N}\mspace{14mu} \cdots \mspace{14mu} b_{{({{N_{b}k} + N_{b} - 1})}{mod}\; N}} \right\rbrack \text{:}\mspace{14mu} k} = 0},1,\cdots,{\frac{N}{N_{b}} - 1}} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},\cdots,W_{1}^{{({N\text{/}N_{b}})} - 1}} \right\}}}} & (4)\end{matrix}$

The second alternative uses overlapping adjacent beam design W₁.

While the non-overlapping design in first alternative gives a compactdesign with minimum number of W₁ matrices, allowing some overlap in beamangles between two X matrices which represents the beam angles withineach polarization group, this may be beneficial to reduce the edgeeffect. The edge effect refers to the phenomena in frequency-selectiveprecoding where the optimum beam angles for the corner RBs within thesub-band are not covered by the same choice of W₁ matrix.

Allowing an overlapping of Nb/2 beam angles between twoconsecutively-indexed W₁ matrices results in the design shown inequation (5). This results in (2N/Nb) W₁ matrices. Note this only worksfor even-valued Nb.

$\begin{matrix}{{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \cdots \mspace{14mu} b_{N - 1}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\frac{2\pi \; {mn}}{N}}},{m = 0},1,{{2\mspace{14mu} n} = 0},1,\cdots,{N - 1}}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({N_{b}k\text{/}2})}{mod}\; N}\mspace{14mu} b_{{({{N_{b}k\text{/}2} + 1})}{mod}\; N}\mspace{14mu} \cdots \mspace{14mu} b_{{({{N_{b}k\text{/}2} + N_{b} - 1})}{mod}\; N}} \right\rbrack \text{:}\mspace{14mu} k} = 0},1,\cdots,{\frac{2N}{N_{b}} - 1}} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},\cdots,W_{1}^{{({2N\text{/}N_{b}})} - 1}} \right\}}}} & (5)\end{matrix}$

Another example allows an overlapping of (Nb−1) beam angles between twoconsecutively-indexed W₁ matrices. This will result in N W₁ matrices.

$\begin{matrix}{{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \cdots \mspace{14mu} b_{N - 1}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\frac{2\pi \; {mn}}{N}}},{m = 0},1,{{2\mspace{14mu} n} = 0},1,\cdots,{N - 1}}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{(k)}{mod}\; N}\mspace{14mu} b_{{({k + 1})}{mod}\; N}\mspace{14mu} \cdots \mspace{14mu} b_{{({k + N_{b} - 1})}{mod}\; N}} \right\rbrack \text{:}\mspace{14mu} k} = 0},1,\cdots,{N - 1}} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},\cdots,W_{1}^{N - 1}} \right\}}}} & (6)\end{matrix}$

For any of these alternatives for W₁ design, the same W₂ design can beapplied for a given value of N and Nb. The following design for W₂ canbe used.

The first part of W₂ utilizes beam selection or beam group selectionwithin each polarization group. The same or different beam(s) can beused for different polarization groups.

The second part of W₂ utilizes co-phasing between two differentpolarization groups. The co-phasing can be done with a unitary vector ormatrix assuming a certain alphabet size, such as Quadrature Phase ShiftKeying (QPSK) or eight-way Phase Shift Keying (8PSK).

The combination of beam selection and co-phasing in W₂ combined with W₁should result in a unitary precoder W=W₁*W₂. Assuming beam (group)selection for different polarization groups and QPSK-based co-phasing,the following W₂ design can be used for rank-1 and 2 regardless of thevalue of Nb. For Rank-1:

$\begin{matrix}{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}} & (7)\end{matrix}$

For Rank-2:

$\begin{matrix}{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}} & (8)\end{matrix}$

The Nb by L (with L denoting the rank) matrix Y is composed of selectionvectors. Denoting e_(n) as an Nb×1 selection vector with all zerosexcept for the n-th element with value 1 (n=1, 2, . . . , Nb), the setof matrix Y (if size Nb) is simply given by equation (9) below.

Yε{e₁,e₂, . . . , e_(Nb)}  (9)

With the designs given in equations (7), (8) and (9), the size of W₂codebook for rank-1 is 4*Nb and for rank-2 is 2*Nb.

For the rank-1 design, co-phasing with larger alphabet size can be done.Although less preferred, this design can be expressed as followsassuming L-PSK co-phasing:

$\begin{matrix}{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{^{j\frac{2\pi}{L}l}Y}\end{bmatrix}},{l = 0},1,\cdots,{L - 1}} \right\}} & (10)\end{matrix}$

For the rank-2 design it is possible to select two different beam anglesinstead of one. This design may be beneficial for ULA scenarios. Therank-2 design for W₂ can be described in the following (more generic)formulation assuming QPSK-based co-phasing:

$\begin{matrix}{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}} & (11)\end{matrix}$

Notice that equation (11) is reduced to the previous examples whenY₁=Y₂=Y.

If Y₁ is not equal to Y₂, the vectors Y₁ and Y₂ should be carefullychosen so that the resulting composite rank-2 precoder is unitary. Thismay not be possible for all combinations of N and Nb such as Nb<N/2.

For rank-2 each of the final product precoders W=W₁*W₂ is a unitarymatrix. This essential property needs to be enforced for higher ranks aswell.

For higher ranks (3, 4, 5 and 6) the benefit of adaptive channeldependent precoding tends to decrease as rank increases. Thus thisinvention only provides codebook designs for ranks 3 and 4. Ranks 5 and6 can use the same W=W₁*W₂ construction with W₁ and W₂ fixed (i.e.size-1 codebook).

For ranks 3 and 4, the adjacent beam designs in equations (4), (5) and(6) can be used as long as it is possible to construct a unitaryprecoder W=W₁*W₂. A prerequisite for this is it is possible to find twoorthogonal column vectors from W₁. From the property of the 3Tx DFTmatrix, this can be achieved when Nb=N/2. Otherwise this conditioncannot be fulfilled. Assume N=12 and Nb=6. Using the overlapping designin equation (6), there are 4 W₁ matrices where the 3Tx DFT beam angles(b) in X for the four W₁ matrices are: {0, 1, 2, 3, 4, 5}, {3, 4, 5, 6,7, 8}, {6, 7, 8, 9, 10, 11}, {9, 10, 11, 0, 1, 2}.

There are only two orthogonal pairs within each of the possible Xmatrices: 1) the first and fifth columns; and 2) the second and sixthcolumns. A possible design for W₂ codebook for ranks 3 and 4 for thiscase is:

For Rank-3:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right),\left( {e_{5},\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack} \right),\left( {e_{6}\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack,e_{5}} \right),\left( {\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack,e_{6}} \right),\left( {\left\lbrack {e_{5}\mspace{14mu} e_{1}} \right\rbrack,e_{1}} \right),\left( {\left\lbrack {e_{6}\mspace{14mu} e_{2}} \right\rbrack,e_{2}} \right),}\end{Bmatrix}}} & (12)\end{matrix}$

For Rank-4:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}},{Y \in \left\{ {\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack,\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right\}}} & (13)\end{matrix}$

Alternatively, a non-adjacent comb-like W₁ design is used for rank-3 and4. This allows more freedom in selecting a pair of orthogonal columns.For higher ranks, it is expected that frequency-selective subbandprecoding gain is small. Thus a non-adjacent design has little impact onthe overall precoding gain and offers richer scattering. This iscompatible with the nature of higher rank transmission. A non-adjacentdesign can be written as follows:

$\begin{matrix}{{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \cdots \mspace{14mu} b_{N - 1}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\frac{2\pi \; {mn}}{N}}},{m = 0},1,{{2\mspace{14mu} n} = 0},1,\cdots,{N - 1}}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{(k)}{mod}\; N}\mspace{14mu} b_{{({k + \frac{N}{N_{b}}})}{mod}\; N}\mspace{14mu} \cdots \mspace{14mu} b_{{({k + {{({N_{b} - 1})}\frac{N}{N_{b}}}})}{mod}\; N}} \right\rbrack \text{:}\mspace{14mu} k} = 0},1,\cdots,{\frac{N}{N_{b}} - 1}} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},\cdots,W_{1}^{{({N\text{/}N_{b}})} - 1}} \right\}}}} & (14)\end{matrix}$

For example if N=12 and Nb=3, there are 4 W₁ matrices where each W₁matrix is composed of a comb of beam angles: {0, 4, 8}, {1, 5, 9}, {2,6, 10}, {3, 7, 11}. For this case the following design for W₂ codebookis applicable:

For Rank-3:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack} \right),\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack} \right),\left( {e_{2}\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack} \right),\left( {e_{3}\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack,e_{1}} \right),\left( {\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack,e_{1}} \right),\left( {\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack,e_{2}} \right),\left( {\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack,e_{2}} \right),\left( {\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack,e_{3}} \right),\left\{ {\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack,e_{3}} \right)}\end{Bmatrix}}} & (15)\end{matrix}$

For Rank-4:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}},{Y \in \left\{ {\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack,\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack,\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack} \right\}}} & (16)\end{matrix}$

It is possible to construct a multi-rank codebook from a subset of adesign. For instance, a multi-rank codebook may be construction usingthe rank-1 design from any of the examples below, except using therank-2 design from another example. The same applies to rank-3 and/orrank-4 designs.

Using a subset or the entirety of the above codebook design examplescombined with some other designs is also covered by this disclosure.

The following are examples of 6Tx codebook design based on augmentingthe Rel. 8 6Tx codebook. While the codebook example covers rank-1 torank-6 (i.e. multi-rank) format, any multi-rank design constructed fromtaking at least one rank-specific codebook(s) from one example and someother rank-specific codebook(s) from other example(s) is permitted. Amulti-rank codebook may be constructed from a subset of a design. Thismay include a multi-rank codebook which uses the rank-1 design from anyof these examples and uses a rank-2 design from another example. For agiven codebook, a combination of a codebook subset of the design for agiven rank with some other design(s) is not precluded. The design forranks 5 and 6 are not given in these examples. Any combination of theseexamples with any rank-5 and/or rank-6 is not precluded.

In a first example the same W₁ based on adjacent overlapping beams isused for all ranks. Assume N=12, Nb=6 and W₁ codebook size-4.

$\begin{matrix}{{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \cdots \mspace{14mu} b_{11}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\frac{2\pi \; {mn}}{12}}},{m = 0},1,{{2\mspace{14mu} n} = 0},1,\cdots,11}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({3k})}{mod}\; 12}\mspace{14mu} b_{{({{3k} + 1})}{mod}\; 12}\mspace{14mu} \cdots \mspace{14mu} b_{{({{3k} + 5})}{mod}\; 12}} \right\rbrack \text{:}\mspace{14mu} k} = 0},1,2,3} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}} & (17)\end{matrix}$

For Rank 1, size-24:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},} & (18) \\{\mspace{79mu} {Y \in \left\{ {e_{1},e_{2},\ldots \mspace{14mu},e_{6}} \right\}}} & \;\end{matrix}$

For Rank 2, size-12:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}},} & (19) \\{Y \in \left\{ {e_{1},e_{2},\ldots \mspace{14mu},e_{6}} \right\}} & \;\end{matrix}$

For Rank 3, size-16:

$\begin{matrix}{\mspace{79mu} {{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\{jY}_{1} & {- {jY}_{2}}\end{bmatrix}}} \right\}},}} & (20) \\{\left( {Y_{1},Y_{2}} \right) \in \begin{Bmatrix}{\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right),\left( {e_{5},\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack} \right),\left( {e_{6},\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right),} \\{\left( {\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack,e_{5}} \right),\left( {\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack,e_{6}} \right),\left( {\left\lbrack {e_{5}\mspace{14mu} e_{1}} \right\rbrack,e_{1}} \right),\left( {\left\lbrack {e_{6}\mspace{14mu} e_{2}} \right\rbrack,e_{2}} \right),}\end{Bmatrix}} & \;\end{matrix}$

For Rank 4, size-4:

$\begin{matrix}{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}},} & (21) \\{Y \in \left\{ {\left\lbrack {e_{1}\mspace{14mu} e_{5}} \right\rbrack,\left\lbrack {e_{2}\mspace{14mu} e_{6}} \right\rbrack} \right\}} & \;\end{matrix}$

In a second example there are different W₁ for different ranks. AssumeN=12.

$\begin{matrix}{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \ldots \mspace{14mu} b_{11}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\; \frac{2\; \pi \; {mn}}{12}}},} & (22) \\{{m = 0},1,{{2\mspace{14mu} n} = 0},1,\ldots \mspace{14mu},11} & \;\end{matrix}$

For Rank 1, W₁ codebook size-4, W₂ codebook size-12, Nb=3 adjacentnon-overlapping:

$\begin{matrix}{\mspace{79mu} {X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({3\; k})}{mod}\; 12}\mspace{14mu} b_{{({{3k} + 1})}{mod}\; 12}\mspace{14mu} b_{{({{3\; k} + 2})}{mod}\; 12}} \right\rbrack:k} = 0},1,2,3} \right\}}} & (23) \\{\mspace{79mu} {{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}} & \; \\{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},} & (24) \\{\mspace{79mu} {Y \in \left\{ {e_{1},e_{2},e_{3}} \right\}}} & \;\end{matrix}$

For Rank 2, W₁ codebook size-4, W₂ codebook size-6, Nb=3 adjacentnon-overlapping:

$\begin{matrix}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({3\; k})}{mod}\; 12}\mspace{14mu} b_{{({{3k} + 1})}{mod}\; 12}\mspace{14mu} b_{{({{3\; k} + 2})}{mod}\; 12}} \right\rbrack:k} = 0},1,2,3} \right\}} & (25) \\{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}} & \; \\{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}},} & (26) \\{Y \in \left\{ {e_{1},e_{2},e_{3}} \right\}} & \;\end{matrix}$

For Rank 3, W₁ codebook size-4, W₂ codebook size-6 (a subset of allpossible 24 W₂ matrices is used), Nb=3 non-adjacent/comb:

$\begin{matrix}{\mspace{79mu} {X^{(k)} \in \left\{ {{{\left\lbrack {b_{k}\mspace{14mu} b_{k + 4}\mspace{14mu} b_{k + 8}} \right\rbrack:k} = 0},1,2,3} \right\}}} & (27) \\{\mspace{79mu} {{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}} & \; \\{\mspace{79mu} {{{W_{2} \in {CB}_{2}} = \left\{ {\frac{1}{\sqrt{2}}\begin{bmatrix}Y_{1} & Y_{2} \\Y_{1} & {- Y_{2}}\end{bmatrix}} \right\}},}} & (28) \\{\left( {Y_{1},Y_{2}} \right) \in \left\{ {\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack} \right),\left( {e_{1},\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack} \right),\left( {e_{2},\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack} \right),\left( {e_{3},\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack} \right)} \right\}} & \;\end{matrix}$

For Rank 4, W₁ codebook size-4, W₂ codebook size-6, Nb=3non-adjacent/comb:

$\begin{matrix}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{k}\mspace{14mu} b_{k + 4}\mspace{14mu} b_{k + 8}} \right\rbrack:k} = 0},1,2,3} \right\}} & (29) \\{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}} & \; \\{{{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\Y & {- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y & Y \\{jY} & {- {jY}}\end{bmatrix}}} \right\}},} & (30) \\{Y \in \left\{ {\left\lbrack {e_{1}\mspace{14mu} e_{2}} \right\rbrack,\left\lbrack {e_{1}\mspace{14mu} e_{3}} \right\rbrack,\left\lbrack {e_{2}\mspace{14mu} e_{3}} \right\rbrack} \right\}} & \;\end{matrix}$

FIG. 8 is a block diagram illustrating internal details of an eNB 1002and a mobile UE 1001 in the network system of FIG. 1. Mobile UE 1001 mayrepresent any of a variety of devices such as a server, a desktopcomputer, a laptop computer, a cellular phone, a Personal DigitalAssistant (PDA), a smart phone or other electronic devices. In someembodiments, the electronic mobile UE 1001 communicates with eNB 1002based on a LTE or Evolved Universal Terrestrial Radio Access Network(E-UTRAN) protocol. Alternatively, another communication protocol nowknown or later developed can be used.

Mobile UE 1001 comprises a processor 1010 coupled to a memory 1012 and atransceiver 1020. The memory 1012 stores (software) applications 1014for execution by the processor 1010. The applications could comprise anyknown or future application useful for individuals or organizations.These applications could be categorized as operating systems (OS),device drivers, databases, multimedia tools, presentation tools,Internet browsers, emailers, Voice-Over-Internet Protocol (VOIP) tools,file browsers, firewalls, instant messaging, finance tools, games, wordprocessors or other categories. Regardless of the exact nature of theapplications, at least some of the applications may direct the mobile UE1001 to transmit UL signals to eNB (base-station) 1002 periodically orcontinuously via the transceiver 1020. In at least some embodiments, themobile UE 1001 identifies a Quality of Service (QoS) requirement whenrequesting an uplink resource from eNB 1002. In some cases, the QoSrequirement may be implicitly derived by eNB 1002 from the type oftraffic supported by the mobile UE 1001. As an example, VOIP and gamingapplications often involve low-latency uplink (UL) transmissions whileHigh Throughput (HTP)/Hypertext Transmission Protocol (HTTP) traffic caninvolve high-latency uplink transmissions.

Transceiver 1020 includes uplink logic which may be implemented byexecution of instructions that control the operation of the transceiver.Some of these instructions may be stored in memory 1012 and executedwhen needed by processor 1010. As would be understood by one of skill inthe art, the components of the uplink logic may involve the physical(PHY) layer and/or the Media Access Control (MAC) layer of thetransceiver 1020. Transceiver 1020 includes one or more receivers 1022and one or more transmitters 1024.

Processor 1010 may send or receive data to various input/output devices1026. A subscriber identity module (SIM) card stores and retrievesinformation used for making calls via the cellular system. A Bluetoothbaseband unit may be provided for wireless connection to a microphoneand headset for sending and receiving voice data. Processor 1010 maysend information to a display unit for interaction with a user of mobileUE 1001 during a call process. The display may also display picturesreceived from the network, from a local camera, or from other sourcessuch as a Universal Serial Bus (USB) connector. Processor 1010 may alsosend a video stream to the display that is received from various sourcessuch as the cellular network via RF transceiver 1020 or the camera.

During transmission and reception of voice data or other applicationdata, transmitter 1024 may be or become non-synchronized with itsserving eNB. In this case, it sends a random access signal. As part ofthis procedure, it determines a preferred size for the next datatransmission, referred to as a message, by using a power threshold valueprovided by the serving eNB, as described in more detail above. In thisembodiment, the message preferred size determination is embodied byexecuting instructions stored in memory 1012 by processor 1010. In otherembodiments, the message size determination may be embodied by aseparate processor/memory unit, by a hardwired state machine, or byother types of control logic, for example.

eNB 1002 comprises a Processor 1030 coupled to a memory 1032, symbolprocessing circuitry 1038, and a transceiver 1040 via backplane bus1036. The memory stores applications 1034 for execution by processor1030. The applications could comprise any known or future applicationuseful for managing wireless communications. At least some of theapplications 1034 may direct eNB 1002 to manage transmissions to or frommobile UE 1001.

Transceiver 1040 comprises an uplink Resource Manager, which enables eNB1002 to selectively allocate uplink Physical Uplink Shared CHannel(PUSCH) resources to mobile UE 1001. As would be understood by one ofskill in the art, the components of the uplink resource manager mayinvolve the physical (PHY) layer and/or the Media Access Control (MAC)layer of the transceiver 1040. Transceiver 1040 includes at least onereceiver 1042 for receiving transmissions from various UEs within rangeof eNB 1002 and at least one transmitter 1044 for transmitting data andcontrol information to the various UEs within range of eNB 1002.

The uplink resource manager executes instructions that control theoperation of transceiver 1040. Some of these instructions may be locatedin memory 1032 and executed when needed on processor 1030. The resourcemanager controls the transmission resources allocated to each UE 1001served by eNB 1002 and broadcasts control information via the PDCCH.

Symbol processing circuitry 1038 performs demodulation using knowntechniques. Random access signals are demodulated in symbol processingcircuitry 1038.

During transmission and reception of voice data or other applicationdata, receiver 1042 may receive a random access signal from a UE 1001.The random access signal is encoded to request a message size that ispreferred by UE 1001. UE 1001 determines the preferred message size byusing a message threshold provided by eNB 1002. In this embodiment, themessage threshold calculation is embodied by executing instructionsstored in memory 1032 by processor 1030. In other embodiments, thethreshold calculation may be embodied by a separate processor/memoryunit, by a hardwired state machine, or by other types of control logic,for example. Alternatively, in some networks the message threshold is afixed value that may be stored in memory 1032, for example. In responseto receiving the message size request, eNB 1002 schedules an appropriateset of resources and notifies UE 1001 with a resource grant.

1. A method of wireless data transmission from a base station having sixantennas to at least one user equipment, comprising the steps of:forming at least one layer of data stream including modulated symbols;precoding the at least one layer of data stream via multiplication withconsecutive first and second precoding matrices; and transmitting theprecoded data stream via the six antennas to the at least one userequipment.
 2. The method of claim 1, wherein: the first precoding matrixW₁ is a block diagonal matrix formed by two identical 3 by Nb matrices,where Nb is the number of distinct Discrete Fourier Transform vectors;and the second precoding matrix W₂ introduces a phase shift between thetwo 3 by Nb matrices and selects a column subset from the firstprecoding matrix.
 3. The method of claim 2, wherein: a set of all thepossible first precoding matrices W1 are as follows: $\begin{matrix}{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \ldots \mspace{14mu} b_{11}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\; \frac{2\; \pi \; {mn}}{12}}},} \\{{{m = 0},1,{{2\mspace{14mu} n} = 0},1,\ldots \mspace{14mu},11}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({3\; k})}{mod}\; 12}\mspace{14mu} b_{{({{3k} + 1})}{mod}\; 12}\mspace{14mu} \ldots \mspace{14mu} b_{{({{3\; k} + 5})}{mod}\; 12}} \right\rbrack:k} = 0},1,2,3} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}}\end{matrix}$ where: B is a 3 by N matrix; X is a 3 by Nb matrix; and m,n and k are index variables.
 4. The method of claim 2, wherein: a set ofall the possible second precoding matrices W₂ are as follows:${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},{Y \in \left\{ {e_{1},e_{2},\ldots \mspace{14mu},e_{6}} \right\}}$where: CB₂ is a codebook for the second precoding matrices W₂; and e_(n)is an Nb by 1 selection vector with all zeros except for the n-thelement with value 1 (n=1, 2, . . . , Nb).
 5. A wireless datatransmission system comprising: a base station having six antennasoperable to form at least one layer of data stream including modulatedsymbols, precode the at least one layer of data stream viamultiplication with consecutive first and second precoding matrices, andtransmit the precoded data stream via six antennas; and at least oneuser equipment operable to receive the transmitted precoded datastreams.
 6. The wireless data transmission system of claim 5, wherein:said base station is further operable to precode the at least one layerof data stream wherein the first precoding matrix W₁ is a block diagonalmatrix formed by two identical 3 by Nb matrices, where Nb is the numberof distinct Discrete Fourier Transform vectors, and the second precodingmatrix W₂ introduces a phase shift between the two 3 by Nb matrices andselects a column subset from the first precoding matrix.
 7. The wirelessdata transmission system of claim 6, wherein: said base station isfurther operable to precode the at least one layer of data streamwherein a set of all the possible first precoding matrices W1 are asfollows: $\begin{matrix}{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \ldots \mspace{14mu} b_{11}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\; \frac{2\; \pi \; {mn}}{12}}},} \\{{{m = 0},1,{{2\mspace{14mu} n} = 0},1,\ldots \mspace{14mu},11}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({3\; k})}{mod}\; 12}\mspace{14mu} b_{{({{3k} + 1})}{mod}\; 12}\mspace{14mu} \ldots \mspace{14mu} b_{{({{3\; k} + 5})}{mod}\; 12}} \right\rbrack:k} = 0},1,2,3} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}}\end{matrix}$ where: B is a 3 by N matrix; X is a 3 by Nb matrix; Nbdenotes the number of adjacent transmit antenna Discrete FourierTransform (DFT) beams; and m, n and k are index variables.
 8. Thewireless data transmission system of claim 6, wherein: said base stationis further operable to precode the at least one layer of data streamwherein a set of all the possible second precoding matrices W₂ are asfollows:${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},{Y \in \left\{ {e_{1},e_{2},\ldots \mspace{14mu},e_{6}} \right\}}$where: CB₂ is a codebook for the second precoding matrices W₂; e_(n) isan Nb by 1 selection vector with all zeros except for the n-th elementwith value 1 (n=1, 2, . . . , Nb); and Nb denotes the number of adjacenttransmit antenna Discrete Fourier Transform (DFT) beams.
 9. A wirelessdata transmission system comprising: a base station having six antennasoperable to form at least one layer of data stream including modulatedsymbols, precode the at least one layer of data stream viamultiplication with consecutive first and second precoding matrices, andtransmit the precoded data stream via six antennas.
 10. The wirelessdata transmission system of claim 9, wherein: said base station isfurther operable to precode the at least one layer of data streamwherein the first precoding matrix W₁ is a block diagonal matrix formedby two identical 3 by Nb matrices, where Nb is the number of distinctDiscrete Fourier Transform vectors, and the second precoding matrix W₂introduces a phase shift between the two 3 by Nb matrices and selects acolumn subset from the first precoding matrix.
 11. The wireless datatransmission system of claim 10, wherein: said base station is furtheroperable to precode the at least one layer of data stream wherein a setof all the possible first precoding matrices W1 are as follows:$\begin{matrix}{{B = \left\lbrack {b_{0}\mspace{14mu} b_{1}\mspace{14mu} \ldots \mspace{14mu} b_{11}} \right\rbrack},{\lbrack B\rbrack_{{1 + m},{1 + n}} = ^{j\; \frac{2\; \pi \; {mn}}{12}}},} \\{{{m = 0},1,{{2\mspace{14mu} n} = 0},1,\ldots \mspace{14mu},11}{X^{(k)} \in \left\{ {{{\left\lbrack {b_{{({3\; k})}{mod}\; 12}\mspace{14mu} b_{{({{3k} + 1})}{mod}\; 12}\mspace{14mu} \ldots \mspace{14mu} b_{{({{3\; k} + 5})}{mod}\; 12}} \right\rbrack:k} = 0},1,2,3} \right\}}{{W_{1}^{(k)} = \begin{bmatrix}X^{(k)} & 0 \\0 & X^{(k)}\end{bmatrix}},{C_{1} = \left\{ {W_{1}^{(0)},W_{1}^{(1)},W_{1}^{(2)},W_{1}^{(3)}} \right\}}}}\end{matrix}$ where: B is a 3 by N matrix; X is a 3 by Nb matrix; Nbdenotes the number of adjacent transmit antenna Discrete FourierTransform (DFT) beams; and m, n and k are index variables.
 12. Thewireless data transmission system of claim 10, wherein: said basestation is further operable to precode the at least one layer of datastream wherein a set of all the possible second precoding matrices W₂are as follows:${{W_{2} \in {CB}_{2}} = \left\{ {{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\Y\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{jY}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- Y}\end{bmatrix}},{\frac{1}{\sqrt{2}}\begin{bmatrix}Y \\{- {jY}}\end{bmatrix}}} \right\}},{Y \in \left\{ {e_{1},e_{2},\ldots \mspace{14mu},e_{6}} \right\}}$where: CB₂ is a codebook for the second precoding matrices W₂; e_(n) isan Nb by 1 selection vector with all zeros except for the n-th elementwith value 1 (n=1, 2, . . . , Nb); and Nb denotes the number of adjacenttransmit antenna Discrete Fourier Transform (DFT) beams.